On subspace methods in system identification and sensor array signal processing
Magnus Jansson · 1997
The common theme of the thesis is the derivation and analysis of subspace parameter estimation methods. In particular, this thesis is concerned with the identification of linear time invariant dynamical systems and the estimation of the directions of arrival (DOAs) using sensor arrays. The first part focuses on sensor array signal processing. The forwardbackward approach has proved quite useful for improving the performance of many suboptimal array processing methods. Herein, it is shown that this approach should not be used with a statistically optimal method such as MODE or WSF. A robust weighted subspace fitting method for a wide class of array perturbation models is derived. The method takes the first order errors due to finite sample effects of the noise and the model perturbation into account in an optimal way to give minimum variance estimates of the DOAs. Interestingly enough, the method reduces to the WSF (MODE) estimator if no model errors are present. On the other hand, when model errors dominate, the proposed method turns out to be equivalent to the “model-errors-only subspace fitting method”. Furthermore, an alternative method known as MAPprox, is also shown to yield minimum variance estimates. A novel subspace-based algorithm for the estimation of the DOAs of uncorrelated emitter signals is derived. The asymptotic variance of the estimates is shown to coincide with the relevant Cramer Rao lower bound. This implies that the method in certain cases has a significantly better performance than methods that do not exploit the a priori information about the signal correlation. Unlike previous techniques, the estimator can be implemented by making use of standard matrix operations only, if the array is uniform and linear. The second part of the thesis deals with the analysis and interpretation of subspace methods for system identification. It is shown that sev-